On Sun, 8 Jul 2012 03:45:33 -0700 (PDT), Jörg <joerg.meier@vint.de> wrote:> Hi group,>> I'm currently dealing with the basics of the Finite Element Method: I want > to compute the strains of an element based on the nodal displacements. The > nodal displacements are given from a FE-Program which is using isoparametric > elements.>> In [1] (section 4.2.5) it is given how to compute the strain vector '{eps}' > using the strain-displacement matrix '[B]' and the nodal displacement vector > '{q}':> {eps} = [B] * {q}>> To compute [B] numerically I have assemble it from several sub-matrices > [B_i] (given at page 23 in [1]). The several [B_i] have to be computed by > inverting the Jacobian matrix [J]. [J] itself is composed of the derivative > of the shape function Ni.>>> What I do not understand:>> - How many [B_i] I have to provide? Is i ranging from 1 to the count of > nodes within the element?

Shortly: Yes. More below.

>> - I can easily derive the shape functions Ni for the local coordinates 's' > or 't'. But in general Ni * d/ds or Ni * d/dt remain dependet on 's' and/or > 't'. Therefore I have to provide a value for 's' and 't' when I numerically > calculate [J]. But what value of 's' and 't' I have to provide for the > current [B_i] ?>

You need to compute [B] in two situations: a) computing stiffnessmatrix, b) computing stress at some point

with row lenght equal to number of element DOF and double ofnumber of shape function (since the same shape functionsapproximate two field u and v). Here number of nodes is equal tonumber of sahpe functions.